Spin-1 condensates at thermal equilibrium: A SU(3) coherent state approach

Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL Research University, UPMC-Sorbonne Universités 11 place Marcelin Berthelot, 75005 Paris, France

Received: 20 February 2015
Accepted: 10 April 2015

Abstract

We propose a theoretical framework based on SU(3) coherent states as a convenient tool to describe the collective state of a Bose-Einstein condensate of spin-1 atoms at thermal equilibrium. We work within the single-mode approximation, which assumes that all atoms condense in the same spatial mode. In this system, the magnetization m_z is conserved to a very good approximation. This conservation law is included by introducing a prior distribution for m_z and constructing a generalized statistical ensemble that preserves its first moments. In the limit of large particle numbers, we construct the partition function at thermal equilibrium and use it to compute various quantities of experimental interest, such as the probability distribution function and moments of the population in each Zeeman state. When N is large but finite (as in typical experiments, where ), we find that fluctuations of the collective spin can be important.